In color space transformations based on three-dimensional (3D) lookup with tetrahedral interpolation, the interpolation stage calculates the estimated [CMYK] output value based on the given CMYK values of the nearest four nodes to the current location in the input 3D space. Such a methodology assumes that the color transformation is relatively smooth and that the nodes are placed close enough such that the transformation is approximately piece-wise linear between adjacent nodes.
The approximation level (and the resulting color transformation accuracy) is generally dependent on the number of nodes, their relative positions, and the non-linearity of the color transformation in a given neighborhood. The interpolation computation equation in accordance with one existing method can be described as follows:Outputi=1/128(128*P0i+Xfrc*ΔXi+Yfrc*ΔYi+Zfrc*ΔZi)                Where iε{C, M, Y, K}.        
The above equation assumes that the CMYK node difference values (ΔX, ΔY, ΔZ) are represented as signed 8-bit numbers, and the fractional position values (Xfrc, Yfrc, Zfrc) within a given tetrahedron are represented as unsigned 8-bit numbers after the subsequent rank ordering described below.
The above equation can be computed per output color component (C, M, Y, and K), where the node delta values (ΔX, ΔY, ΔZ) are dependent on the tetrahedron containing the mapped input point in the input color space (e.g., in (L, a, b) or (Y, Cb, Cr)).
Note that, in general, the chrominance values (a, b) or (Cb, Cr) are signed numbers while the luminance values (L or Y) are unsigned numbers.
In one application, each cube of the input color space can be divided into six non-overlapping tetrahedrons of the same size. Alternatively, the space can be divided into five tetrahedrons (i.e., a fewer number), but in this case the center tetrahedron has a larger size and this somewhat complicates the calculations. Thus, the focus can be on the six tetrahedron case. Table 1 below illustrates the node value delta computation for all possible tetrahedrons with reference to the existing method.
TABLE 1Order in which the node values Δs are computedTetrahedronΔXΔYΔZ1P1-P0P2-P1P3-P22P1-P0P3-P2P2-P13P2-P1P3-P2P1-P04P2-P1P1-P0P3-P25P3-P2P1-P0P2-P16P3-P2P2-P1P1-P0
The specific tetrahedron in which the input location resides can be easily determined by simply ordering the fractional delta values (Xfrc, Yfrc, Zfrc) in rank order. The interpolation algorithm computes the output value using rounding and limiting the final result to the preferred output range (e.g., between 0 and 255 for 8-bit output). After the interpolated CMYK point has been calculated, each of its color components can be used as an address to four different 1D lookup tables. These lookup tables provide a means to linearize the main CMYK color interpolation table of node values with respect to the individual {C, M, Y, K} color response. In addition, the 1D lookup tables can be used to compensate for changes in the individual {C, M, Y, K} tone reproduction curve as the machine drifts over time and/or the level of toner/ink is depleted without having to re-calibrate the node positions of the main color tables. The values accessed from the four lookup tables represent the adjusted CMYK values that comprise the final output value.
The entire color interpolation method in accordance with one existing method can then be described as following: for each output channel (C, M, Y, and K), four output values representing the nearest nodes to the mapped Lab or YCC input point are looked-up in a table and used in a tetrahedral interpolation step to find the approximated CMYK output value. The resulting output value is then adjusted by a byte-to-byte mapping using four 1-D lookup tables.
Color space transformation via 3D Lookup table with tetrahedral interpolation is a well-known algorithm for converting from one color space (e.g., RGB or Lab) to another (e.g., CMYK for printing). In software implementations on general purpose processors, for example, the computational steps are processed in sequential fashion, one color separation at a time. Although the fractional position within a specific tetrahedron is the same for each color separation, the node values are different, thus requiring individual calculations per color separation. In contrast, the algorithm can be efficiently implemented in hardware by packing the data and processing the transformation of the color channels in parallel. By taking advantage of this property, it can be demonstrated that certain media processors with data-level parallelism can deliver higher-performance color space transformation relative to general purpose processors and common hardware implementations.
One known prior art application involves interpolation techniques for improved efficiency and speed in performing color space conversions. In such a case, a radial interpolation technique can accomplish an interpolation by generating successive subcubes. A value of a vertex of the final subcube generated can be used as the result of the interpolation. Subcubes are generated by averaging a selected vertex value with the vertex values of each of the remaining vertices. A pruned radial interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the radial interpolation. A tetrahedral interpolation technique accomplishes an interpolation by generating successive subcubes.
A value of a vertex of the final subcube generated can be used as the result of the interpolation. Subcubes are generated by applying a mathematical relationship which allows computation of subcube vertex values through a series of logical AND, logical OR and averaging operations. A pruned tetrahedral interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the tetrahedral interpolation. A common hardware implementation of pruned radial interpolation and pruned tetrahedral interpolation uses the common hardware structure of the two techniques with multiplexing of the input vertex values to allow performance of either a pruned radial interpolation or a pruned tetrahedral interpolation. Non-symmetric pruned radial and Non-symmetric pruned tetrahedral interpolation permit interpolation using interpolation data values distributed throughout the color space with a resolution that varies according to characteristics of the color space. Multiplexing of the interpolation data values to the non-symmetric pruned radial interpolation hardware and to the non-symmetric pruned tetrahedral interpolation hardware allows for a common hardware implementation.
Another prior art technique involves tetrahedral interpolation by rewriting the interpolation in terms of ordered differentials and color differences to lower the computational complexity.
One of the problems with these prior art techniques is that such methodologies and related devices are inefficient and cannot be easily adapted to a wide range of image processing applications. In order to overcome these problems, it is believed that the embodiments disclosed herein can be implemented for increased efficiency in both processing and hardware applications.